A geometric graph is a weighted graph in the plane where every vertex \(v\)  has coordinates \((x_v, y_v)\)  and the weight of an edge between any two vertices is the Euclidean distance between its endpoints. A geometric spanner is defined to be a subgraph of the complete geometric graph where the shortest path distance between any two vertices is at most the Euclidean distance between these two vertices multiplied by a constant \(t\) . The smallest constant \(t\)  for which this property holds is called the spanning ratio or stretch factor of the geometric spanner. A comprehensive overview on the topic of geometric spanners can be found in the book by Narasimhan and Smid [1]} and the survey by Bose and Smid [2]}.
